If you're interested in getting started in showing, I'd purchase the
American Standard of Perfection from the American Poultry Association. This will give you the defects and disqualifications for each breed, and will tell you what an ideal example of the breed would look like.
Rhode Island Reds and American Games are rather challenging birds to show. If you have Rhode Island Reds from a hatchery, you should not show them. Rhode Island REds have to be a deep mahogany color. The color is very difficult to breed for; light colored ones are not showable, but if you get them too dark, black feathers can show through, and that is a serious defect.
American Game cocks have to be dubbed (that is, the comb, wattles, and earlobes mostly removed). This is required; if you do not do this, your birds will be disqualified. American Game should feel hard and muscular, so you do not want to overfeed them.
If you want to learn more about the markings found on cage cards, here are two links:
http://pathfindersfarm.com/Cagecards.html
http://pathfindersfarm.com/Cagecards2.html
Hope this helps!